## [1] "Run Completed at 2018-02-07 14:55:02"
\[ Yobs_{i,j} \sim Bernoulli(N(0,1.68)) \]
Note that this is a random probability of interaction on a per observation basis. This is different than a random link model. If we are interested in a binary network, a random interaction probability model will lead to a link probability of 1-(1/2)^n in n sampling events.
## sink("models/SpeciesIdentity.jags")
## cat("
## model {
##
## for (x in 1:Nobs){
##
## #observation
## logit(s[x])<-alpha[Bird[x],Plant[x]]
## Yobs[x] ~ dbern(s[x])
##
## }
##
## #Assess Model Fit - Predict remaining data
## for(x in 1:Nnewdata){
##
## #Generate prediction
## logit(snew[x])<-alpha[NewBird[x],NewPlant[x]]
## Ynew_pred[x]~dbern(snew[x])
##
## #Assess fit, proportion of corrected predicted observations
## Enew[x]<-abs(Ynew[x]-Ynew_pred[x])
##
## }
##
## #Priors
##
## #Species level priors
## for (i in 1:Birds){
## for (j in 1:Plants){
##
## #Intercept
## #logit prior, then transform for plotting
## alpha[i,j] ~ dnorm(0,0.386)
## }
## }
##
## #derived posterior predictive error
## fitnew<-sum(Enew[])
## }
## ",fill=TRUE)
##
## sink()
## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 0
## Unobserved stochastic nodes: 1955
## Total graph size: 7448
##
## Initializing model
\[ Yobs_{i,j} \sim Bernoulli(\lambda_{i,j}) \]
## sink("models/SpeciesIdentity.jags")
## cat("
## model {
##
## for (x in 1:Nobs){
##
## #observation
## logit(s[x])<-alpha[Bird[x],Plant[x]]
## Yobs[x] ~ dbern(s[x])
##
## }
##
## #Assess Model Fit - Predict remaining data
## for(x in 1:Nnewdata){
##
## #Generate prediction
## logit(snew[x])<-alpha[NewBird[x],NewPlant[x]]
## Ynew_pred[x]~dbern(snew[x])
##
## #Assess fit, proportion of corrected predicted observations
## Enew[x]<-abs(Ynew[x]-Ynew_pred[x])
##
## }
##
## #Priors
##
## #Species level priors
## for (i in 1:Birds){
## for (j in 1:Plants){
##
## #Intercept
## #logit prior, then transform for plotting
## alpha[i,j] ~ dnorm(0,0.386)
## }
## }
##
## #derived posterior predictive error
## fitnew<-sum(Enew[])
## }
## ",fill=TRUE)
##
## sink()
## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 830
## Unobserved stochastic nodes: 1125
## Total graph size: 7448
##
## Initializing model
Observation Model:
\[ Yobs_{i,j,k,d} \sim Binomial(N_{i,j,k},\omega_i) \]
Process Model:
\[ N_{i,j,k} \sim Binomial(\lambda_{i,j}) \] \[ Yobs_{i,j} \sim Bernoulli(\lambda_{i,j}) \]
## sink("models/SpeciesIdentity_Detect.jags")
## cat("
## model {
##
## #True interaction probability for each bird, plant
## for (i in 1:Birds){
## for(j in 1:Plants){
## logit(s[i,j])<-alpha[i,j]
## }
## }
##
## #Observation Model
## for (x in 1:Nobs){
##
## #Detection Process
## z[x] ~ dbern(detect[Bird[x]])
##
## #Observation
## p[x]<-z[x] * s[Bird[x],Plant[x]]
## Yobs[x] ~ dbern(p[x])
## }
##
## #Assess Model Fit - Predict remaining data
##
## for(x in 1:Nnewdata){
##
## #Generate prediction
## znew[x] ~ dbern(detect[NewBird[x]])
## pnew[x] <- znew[x]*s[NewBird[x],NewPlant[x]]
##
## #Predicted observation
## Ynew_pred[x]~dbern(pnew[x])
##
## #Assess fit, proportion of corrected predicted links
## Enew[x]<-abs(Ynew[x]-Ynew_pred[x])
##
## }
##
## #Priors
## #Observation model
## #Detect priors, logit transformed - Following lunn 2012 p85
## for(x in 1:Birds){
## logit(detect[x])<-dcam[x]
## dcam[x]~dnorm(omega_mu,omega_tau)
## }
##
## #Process Model
## #Species level priors
## for (i in 1:Birds){
## for (j in 1:Plants){
## #Logit Intercept
## alpha[i,j] ~ dnorm(0,0.386)
## }
## }
##
## #OBSERVATION PRIOR
## omega_mu ~ dnorm(0,0.386)
## omega_tau ~ dunif(0,10)
##
## #derived posterior predictive error
## fitnew<-sum(Enew[])
##
## }
## ",fill=TRUE)
##
## sink()
## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 830
## Unobserved stochastic nodes: 2647
## Total graph size: 10491
##
## Initializing model
# Incorporating species occurrence
If species co-occurrence is a prerequisite for interaction, then the absence of interactions may stem either from a lack of detectability or species absence. We can jointly model the presence of species as a function of elevation and then existance of an interaction.
Observation Model:
\[ Yobs_{i,j,k,d} \sim Binomial(N_{i,j,k},\omega_i) \]
Process Model:
\[ N_{i,j,k} \sim Binomial(\lambda_{i,j}) \] \[ Yobs_{i,j} \sim Bernoulli(\lambda_{i,j}) \]
## sink("models/SpeciesIdentity_Detect_Elevation.jags")
## cat("
## model {
##
## #Ecological Process Model
## #True State for each bird, plant, camera
## for (i in 1:Birds){
## for(j in 1:Plants){
## for(k in 1:Cameras){
##
## #Occurrence
## logit(psi[i,j,k])<-alpha_occ[i] + beta_occ[i] * elevation[k] + beta2_occ[i] * elevation[k]^2
## occ[i,j,k] ~ dbern(psi[i,j,k])
##
## #Interaction
## logit(s[i,j,k])<-alpha[i,j]
##
## #Conditional probability of interaction|occurrence
## rho[i,j,k] <- s[i,j,k] * occ[i,j,k]
## }
## }
## }
##
## #Observation Model
## for (x in 1:Nobs){
##
## #Detection Process
## z[x] ~ dbern(detect[Bird[x]])
##
## #Observation, conditional on detection and occurrence.
## p[x]<-z[x] * rho[Bird[x],Plant[x],Camera[x]]
## Yobs[x] ~ dbern(p[x])
##
## #Observed discrepancy
## #E[x]<-abs(Yobs[x]- s[Bird[x],Plant[x],Camera[x]])
## }
##
## #Assess Model Fit - Predict remaining data
##
## for(x in 1:Nnewdata){
##
## #Generate prediction
## znew[x] ~ dbern(detect[NewBird[x]])
## pnew[x] <- znew[x]*rho[NewBird[x],NewPlant[x],NewCamera[x]]
##
## #Predicted observation
## Ynew_pred[x]~dbern(pnew[x])
##
## #Assess fit, proportion of corrected predicted links
## Enew[x]<-abs(Ynew[x]-Ynew_pred[x])
##
## }
##
## #Priors
##
## #Occurrence model
## for(x in 1:Birds){
## alpha_occ[x] ~ dnorm(0,0.386)
## beta_occ[x] ~ dnorm(0,0.386)
## beta2_occ[x] ~ dnorm(0,0.386)
## }
##
## #Observation model
## #Detect priors, logit transformed - Following lunn 2012 p85
## for(x in 1:Birds){
## logit(detect[x])<-dcam[x]
## dcam[x]~dnorm(omega_mu,omega_tau)
## }
##
## #Process Model
## for (i in 1:Birds){
## for (j in 1:Plants){
## #Intercept
## #logit prior, then transform for plotting
## alpha[i,j] ~ dnorm(0,0.386)
## }
## }
##
## #Observation group prior
## omega_mu ~ dnorm(0,0.386)
## omega_tau ~ dunif(0,10)
##
## #derived posterior predictive check
## fitnew<-sum(Enew[])
##
## }
## ",fill=TRUE)
##
## sink()
## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 830
## Unobserved stochastic nodes: 35542
## Total graph size: 81903
##
## Initializing model
##
## user system elapsed
## 13.165 0.099 13.418
## # A tibble: 4 x 4
## # Groups: Model [4]
## Model Presence Absence p
## <chr> <int> <int> <dbl>
## 1 Random 2472 378 86.7
## 2 Species 2025 825 71.1
## 3 Species_Detect 574 2276 20.1
## 4 Species_Detect_Elevation 617 2233 21.6
## [1] "True presence rate is: 9.1"
Dashed line is the observed network from the time-series.
How much to do here.
Split data into wet (November - May) versus dry season (June - October)
## sink("models/SpeciesIdentity_Detect_Elevation_Beta.jags")
## cat("
## model {
##
## #Ecological Process Model
## #True State for each bird, plant, camera
## for (i in 1:Birds){
## for(j in 1:Plants){
## for(k in 1:Cameras){
##
## #Occurrence
## logit(psi[i,j,k])<-alpha_occ[i] + beta_occ[i] * elevation[k] + beta2_occ[i] * elevation[k]^2
## occ[i,j,k] ~ dbern(psi[i,j,k])
##
## #Interaction
## logit(s[i,j,k])<-alpha[i,j] + beta_season[i,j] *Season[k]
##
## #Conditional probability of interaction|occurrence
## rho[i,j,k] <- s[i,j,k] * occ[i,j,k]
## }
## }
## }
##
## #Observation Model
## for (x in 1:Nobs){
##
## #Detection Process
## z[x] ~ dbern(detect[Bird[x]])
##
## #Observation, conditional on detection and occurrence.
## p[x]<-z[x] * rho[Bird[x],Plant[x],Camera[x]]
## Yobs[x] ~ dbern(p[x])
##
## #Observed discrepancy
## #E[x]<-abs(Yobs[x]- s[Bird[x],Plant[x],Camera[x]])
## }
##
## #Assess Model Fit - Predict remaining data
##
## for(x in 1:Nnewdata){
##
## #Generate prediction
## znew[x] ~ dbern(detect[NewBird[x]])
## pnew[x] <- znew[x]*rho[NewBird[x],NewPlant[x],NewCamera[x]]
##
## #Predicted observation
## Ynew_pred[x]~dbern(pnew[x])
##
## #Assess fit, proportion of corrected predicted links
## Enew[x]<-abs(Ynew[x]-Ynew_pred[x])
##
## }
##
## #Priors
##
## #Occurrence model
## for(x in 1:Birds){
## alpha_occ[x] ~ dnorm(0,0.386)
## beta_occ[x] ~ dnorm(0,0.386)
## beta2_occ[x] ~ dnorm(0,0.386)
## }
##
## #Observation model
## #Detect priors, logit transformed - Following lunn 2012 p85
## for(x in 1:Birds){
## logit(detect[x])<-dcam[x]
## dcam[x]~dnorm(omega_mu,omega_tau)
## }
##
## #Process Model
## for (i in 1:Birds){
## for (j in 1:Plants){
## #Interaction probability
## alpha[i,j] ~ dnorm(0,0.386)
## #Effect of season
## beta_season[i,j] ~ dnorm(0,0.386)
## }
## }
##
## #Observation group prior
## omega_mu ~ dnorm(0,0.386)
## omega_tau ~ dunif(0,10)
##
## #derived posterior predictive check
## #fitnew<-sum(Enew[])
##
## }
## ",fill=TRUE)
##
## sink()
## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 830
## Unobserved stochastic nodes: 35992
## Total graph size: 84674
##
## Initializing model
##
## user system elapsed
## 17.695 0.189 18.296
Dissimilairty in interactions (Beta_WN from Poisot 2012) Dashed line is the observed network from the time-series.
Note that this is really a measure of dissimilairty in one level (hummimngbirds), as the dissimilarity in plants is fixed by the sampling protocol. While there be a correlation between the species pool and the chosen plant to film, this is filtered by a human placing a camera at that plant, and as such isn’t a true measure of plant dissimiality.
Create a kind of venn diagram on PCA of model similarity based on per link discrepency.
## # A tibble: 22 x 3
## # Groups: Model [4]
## Model mean pair
## <chr> <dbl> <chr>
## 1 Species -1.00 Collared Inca_Bomarea pardina
## 2 Species_Detect -1.00 Tawny-bellied Hermit_Fuchsia macrostig…
## 3 Species_Detect -1.00 Tawny-bellied Hermit_Heliconia burleana
## 4 Species_Detect -1.00 Violet-tailed Sylph_Palicourea acetoso…
## 5 Species_Detect -0.950 Tawny-bellied Hermit_Centropogon solan…
## 6 Species_Detect -0.950 Tawny-bellied Hermit_Columnea kucyniak…
## 7 Species_Detect -0.950 Violet-tailed Sylph_Gasteranthus later…
## 8 Species_Detect -0.950 Violet-tailed Sylph_Guzmania jaramilloi
## 9 Species_Detect -0.950 Violet-tailed Sylph_Kohleria affinis
## 10 Species_Detect_Elevation -0.950 Collared Inca_Bomarea pardina
## # ... with 12 more rows
Without random model